What is a Singularity?

How do they occur? Mathematically, the solver uses matrices to represent the elastic field (displacements of the elements). When a highly localized load is applied, the gradients of the displacement vectors begin to diverge, causing the roots of the matrices to go to infinity. For a simplified explanation, see the stress equation below. Stress goes to infinity due to force applied in a very small area.

Where do Singularities occur?

Singularities are usually seen at points, edges, or reentrant corners. Reentrant corners are interior corners, with angles pointing into the part. The high stress concentrations are usually seen near 90 degree corners, but can potentially occur for any angle less than 180 degrees.

Why don’t they occur in real life?

Think of the common case of singularities created on interior corners. In software, that corner is perfectly sharp. In real life, there will always be a slight bend. Also, the part may deform slightly, or “slip”, and allow the faces of the corner to slide against each other. The slight bend and additional friction allow for a converging stress.
“Adjust your legend’s color settings to grey out above the material’s yield point. This prevents singularities from overshadowing other important stress results!” – Joe Engineer, Know It All, GoEngineer